A Markov chain approximation scheme for option pricing under skew diffusions

In this paper, we propose a general valuation framework for option pricing problems related to skew diffusions based on a continuous-time Markov chain approximation to the underlying stochastic pro...

[1]  P. Pigato.  Extreme at-the-money skew in a local volatility model , 2019, Finance and Stochastics.

[2]  Antoine Lejay,et al.  Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps , 2012, J. Comput. Phys..

[3]  Yongjin Wang,et al.  Pricing European vanilla options under a jump-to-default threshold diffusion model , 2018, J. Comput. Appl. Math..

[4]  Suxin Wang,et al.  First hitting times for doubly skewed Ornstein–Uhlenbeck processes , 2015 .

[5]  Zhenyu Cui,et al.  Transform Analysis for Markov Processes and Applications: An Operator-based Approach , 2019, SSRN Electronic Journal.

[6]  Stefan Blei,et al.  On symmetric and skew Bessel processes , 2012 .

[7]  Artur Sepp,et al.  Filling the Gaps , 1962, Mental health.

[8]  Zhenyu Cui,et al.  Pricing Timer Options , 2010 .

[9]  W. Schoutens,et al.  Asymmetric skew Bessel processes and their applications to finance , 2006 .

[10]  A. Lejay,et al.  A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients , 2006, math/0603214.

[11]  Zhenyu Cui,et al.  An efficient and stable method for short maturity Asian options , 2018, Journal of Futures Markets.

[12]  Alexandru Badescu,et al.  Closed-form variance swap prices under general affine GARCH models and their continuous-time limits , 2017, Ann. Oper. Res..

[13]  M. Broadie,et al.  American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods , 1996 .

[14]  Silverio Foresi,et al.  Price Barriers and the Dynamics of Asset Prices in Equilibrium , 1996, Journal of Financial and Quantitative Analysis.

[15]  Yongjin Wang,et al.  Skew Ornstein-Uhlenbeck processes and their financial applications , 2015, J. Comput. Appl. Math..

[16]  Fernando Zapatero,et al.  Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier , 2000, Journal of Financial and Quantitative Analysis.

[17]  Olivier Menoukeu-Pamen,et al.  Efficient Piecewise Trees for the Generalized Skew Vasicek Model with Discontinuous Drift , 2017 .

[18]  Song-Ping Zhu,et al.  A new closed-form formula for pricing European options under a skew Brownian motion , 2017 .

[19]  Antoine Lejay.  On the constructions of the skew Brownian motion , 2006 .

[20]  Damiano Rossello,et al.  Arbitrage in skew Brownian motion models , 2012 .

[21]  S. Satchell,et al.  Skew Brownian Motion and Pricing European Options , 2007 .

[22]  N. Portenko,et al.  Diffusion Processes with Generalized Drift Coefficients , 1979 .

[23]  Vadim Linetsky,et al.  Pricing and Hedging Path-Dependent Options Under the CEV Process , 2001, Manag. Sci..

[24]  Aleksandar Mijatović,et al.  CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES , 2009, 0908.4028.

[25]  Vadim Shcherbakov,et al.  DENSITY OF SKEW BROWNIAN MOTION AND ITS FUNCTIONALS WITH APPLICATION IN FINANCE , 2014, 1407.1715.

[26]  Stephen Taylor,et al.  Pricing Discretely Monitored Barrier Options under Markov Processes through Markov Chain Approximation , 2020, The Journal of Derivatives.

[27]  Giuseppe Bertola,et al.  Target Zones and Realignments , 1990 .

[28]  Arturo Kohatsu-Higa,et al.  The Parametrix Method for Skew Diffusions , 2016 .

[29]  Marti G. Subrahmanyam,et al.  Pricing and Hedging American Options: A Recursive Integration Method , 1995 .

[30]  Alexandru Badescu,et al.  Variance swaps valuation under non-affine GARCH models and their diffusion limits , 2018, Quantitative Finance.

[31]  Hoi Ying Wong,et al.  Option Pricing with Threshold Mean Reversion , 2017 .

[32]  Zhenyu Cui,et al.  Equity-Linked Annuity Pricing with Cliquet-Style Guarantees in Regime-Switching and Stochastic Volatility Models with Jumps , 2017 .

[33]  Lingfei Li,et al.  Error analysis of finite difference and Markov chain approximations for option pricing , 2017 .

[34]  Antoine Lejay,et al.  One-dimensional skew diffusions: explicit expressions of densities and resolvent kernels , 2015 .

[35]  Chihoon Lee,et al.  On pricing barrier control in a regime-switching regulated market , 2018, Quantitative Finance.

[36]  Daniel Sheldon,et al.  First Passage Time of Skew Brownian Motion , 2010, Journal of Applied Probability.

[37]  Shiyu Song,et al.  On First Hitting Times for Skew CIR Processes , 2016 .

[38]  P. Krugman,et al.  Target Zones and Exchange Rate Dynamics , 1991 .

[39]  Curt Randall,et al.  Pricing Financial Instruments: The Finite Difference Method , 2000 .

[40]  Zhenyu Cui,et al.  Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model , 2017 .

[41]  Guangli Xu,et al.  A simple trinomial lattice approach for the skew-extended CIR models , 2017 .

[42]  Duy Nguyen,et al.  Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing , 2019 .

[43]  Zhenyu Cui,et al.  A General Framework for Time-Changed Markov Processes and Applications , 2018, Eur. J. Oper. Res..

[44]  J. Ramírez.  Multi-skewed Brownian motion and diffusion in layered media , 2011 .

[45]  Zhenyu Cui,et al.  Martingale Property and Pricing for Time-homogeneous Diffusion Models in Finance , 2013 .

[46]  Antoine Lejay,et al.  Statistical estimation of the Oscillating Brownian Motion , 2017, Bernoulli.

[47]  Carole Bernard,et al.  Prices and Asymptotics for Discrete Variance Swaps , 2013, 1305.7092.

[48]  Kin Lam,et al.  A threshold stochastic volatility model , 2002 .

[49]  J. Harrison,et al.  On Skew Brownian Motion , 1981 .

[50]  Zhenyu Cui,et al.  A General Valuation Framework for SABR and Stochastic Local Volatility Models , 2018, SIAM J. Financial Math..

[51]  N. Frikha.  On the weak approximation of a skew diffusion by an Euler-type scheme , 2016, Bernoulli.

[52]  J. Gall,et al.  One — dimensional stochastic differential equations involving the local times of the unknown process , 1984 .

[53]  M. Yor,et al.  PRICING AND HEDGING DOUBLE-BARRIER OPTIONS: A PROBABILISTIC APPROACH , 1996 .

[54]  R. Glen Donaldson,et al.  Price Barriers in the Dow Jones Industrial Average , 1993, Journal of Financial and Quantitative Analysis.

[55]  N. Kunitomo,et al.  Pricing Options With Curved Boundaries , 1992 .

[56]  Paavo Salminen,et al.  On the local time process of a skew Brownian motion , 2018, Transactions of the American Mathematical Society.

[57]  Zhenyu Cui,et al.  INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS , 2017 .

[58]  Tak Kuen Siu,et al.  A self-exciting threshold jump–diffusion model for option valuation , 2016 .

[59]  Pierre Etor'e,et al.  Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators , 2016, Stochastic Processes and their Applications.

[60]  Zhenyu Cui,et al.  A Unified Approach to Bermudan and Barrier Options Under Stochastic Volatility Models with Jumps , 2017 .

[61]  Tse-Chun Lin,et al.  How the 52-Week High and Low Affect Option-Implied Volatilities and Stock Return Moments , 2011 .

[62]  Carole Bernard,et al.  On the Martingale Property in Stochastic Volatility Models Based on Time‐Homogeneous Diffusions , 2017 .

[63]  William Feller,et al.  Generalized second order differential operators and their lateral conditions , 1957 .

[64]  Duy Nguyen,et al.  A General Framework for Discretely Sampled Realized Variance Derivatives in Stochastic Volatility Models with Jumps , 2017, Eur. J. Oper. Res..

[65]  Michael Sorensen,et al.  DIFFUSION MODELS FOR EXCHANGE RATES IN A TARGET ZONE , 2007 .

[66]  A. Lejay,et al.  A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data , 2017, International Journal of Theoretical and Applied Finance.

[67]  Konstantinos Skindilias,et al.  AN IMPROVED MARKOV CHAIN APPROXIMATION METHODOLOGY: DERIVATIVES PRICING AND MODEL CALIBRATION , 2014 .

[68]  Shiyu Song,et al.  Some properties of doubly skewed CIR processes , 2016 .

[69]  Kung-Sik Chan,et al.  Option Pricing with Threshold Diffusion Processes , 2016 .

[70]  Yingxu Tian,et al.  Skew CIR process, conditional characteristic function, moments and bond pricing , 2018, Appl. Math. Comput..

[71]  Iecn Umr Vandoeuvre-les-Nancy F Cnrs,et al.  Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps , 2012 .